6,696 research outputs found
q-Differential equations for q-classical polynomials and q-Jacobi-Stirling numbers
No full textWe introduce, characterise and provide a combinatorial interpretation for the so-called q-Jacobi–Stirling numbers.
This study is motivated by their key role in the (reciprocal) expansion of any power of a second order
q-differential operator having the q-classical polynomials as eigenfunctions in terms of other even order operators,
which we explicitly construct in this work. The results here obtained can be viewed as the q-version of
those given by Everitt et al. and by the first author, whilst the combinatorics of this new set of numbers is a
q-version of the Jacobi–Stirling numbers given by Gelineau and the second author
Postać n-tej iteracji operatora q = f d/dx
No full textArtykuł nie zawiera streszczeniaMotivated by applications in linear dynamical systems, the author studies q^n(f), where q is the operator f●(d/dx) and qn is its n-th iteration. q^n(f) is a polynomial F(f(0),f(1),...,f(n)) in the derivatives f(0)=f,...,f(n) of f with integer coefficients. Special attention is paid to determining the coefficients of F. The author presents algorithms for computing the coefficients and also shows that the sum of all coefficients of F equals n!. The paper ends with some remarks on the number of coefficients of F, which is related to the number-theoretic unrestricted partition function
Sous-facteurs de L(F∞) d'indice 4cos2π/n,n≥3
No full textLet Q be a factor of type II1, λ a number in the Jones discrete series {4cosπ/m:m≥3}, and {ei} the Jones projections associated with λ. Denote by A2n and A1n the finite-dimensional von Neumann algebras generated, respectively, by {1,e2,⋯,en} and {1,e1,⋯,en}, with the corresponding traces. The author shows that, for n sufficiently large, the index of the inclusion An=(Q⊗A2n)∗A2nA1n⊂(Q⊗A2n+1)∗A2n+1A1n+1=An+1 is equal to λ (here ∗ denotes the reduced, amalgamated free product of the algebras in question). Using the random matrix model of Voiculescu, he proves that if Q is the von Neumann algebra L(F∞) of the free group with infinitely many generators, then An is isomorphic to L(F∞).
The two facts together imply the existence, for any λ in the Jones discrete series, of an irreducible subfactor of L(F∞) of index λ. This constitutes the first example of a nonhyperfinite, non-Γ II1 factor such that its Jones invariant is fully computable (the existence of nonirreducible subfactors of L(F∞) for any index ≥4 is a simple consequence of known results)
Stability of Power Law cosmological model in f(Q) gravity
No full textIn the present study, we have described the accelerated cosmological models of the universe in f(Q) gravity. In f(Q) gravity, the gravitational field equations are modified by a function of the non-metricity tensor, which characterizes the deviation of the affine connection from the metric compatibility condition. We have considered two different forms of f(Q) gravity as f(Q) = \beta + \alpha \, Q^{(n+1)} and f(Q) = \beta \, Q + \alpha \, Q^{n} to explain the dynamics of the expanding universe. We have discussed the dynamics of the universe through graphical representation by considering the power law ( ). The free parameters of {\color{red}the} models are fitted {\color{red}with} the latest observational data set of {\color{red} Observational Hubble Data} (OHD), consisting of 57 points, using statistical analysis based on the MCMC method. The best-fitted values for the model’s parameter are estimated as H_0 = 67.3 \pm 1.1, m = 1.0213 \pm 0.0071, and k = 65.4 \pm 1.1. The parameters of the derived model, like energy density, isotropic pressure, EoS parameter, and jerk parameter, are discussed. We have described the energy conditions to explain the viability of the considered models. We have also verified the stability of the derived model through perturbation analysis.The presentation of the authors' names and (or) special characters in the title of the pdf file of the accepted manuscript may differ slightly from what is displayed on the item page. The information in the pdf file of the accepted manuscript reflects the original submission by the author
q-Fibonacci sequence spaces and related matrix transformations
No full textIn this paper, we define the sequence spaces ?p(F^ q) (1 ? p< ?) , ??(F^ q) , c(F^ q) and c(F^ q) by using q-Fibonacci band matrix F^ q defined by F^q=F^nk(q)={-Fn+1(q)-1qnFn(q),k=n-1Fn+2(q)-1qnFn(q),k=n0,otherwise(k,n?N).We study some topological properties and give some inclusion relations for these spaces. In addition, we build a bases for the space ?p(F^ q) , compute ?-, ?-, ?- duals of the same space, characterize some matrix classes and examine some geometric properties. © 2022, The Author(s) under exclusive licence to Korean Society for Informatics and Computational Applied Mathematics
The Vector-Valued Big q -Jacobi Transform
No full textBig q-Jacobi functions are eigenfunctions of a second-order q-difference operator L. We study L as an unbounded self-adjoint operator on an L-2-space of functions on R with a discrete measure. We describe explicitly the spectral decomposition of L using an integral transform F with two different big q-Jacobi functions as a kernel, and we construct the inverse of F.Delft Institute of Applied MathematicsElectrical Engineering, Mathematics and Computer Scienc
Tuning the Q -factor of nanomechanical string resonators by torsion support design
No full textIn recent years, the Q-factor of Si 3 N 4 nanomechanical resonators has significantly been increased by soft-clamping techniques using large and complex support structures. To date, however, obtaining similar performance with smaller supports has remained a challenge. Here, we make use of torsion beam supports to tune the Q-factor of Si 3 N 4 string resonators. By design optimization of the supports, we obtain a 50% Q-factor enhancement compared to the standard clamped-clamped string resonators. By performing experimental and numerical studies, we show that further improvement of the Q-factor is limited by a trade-off between maximizing stress and minimizing torsional support stiffness. Thus, our study also provides insight into dissipation limits of high-stress string resonators and outlines how advanced designs can be realized for reaching ultimate f 0 × Q product while maintaining a small footprint.</p
Roughness Induced Boundary Layer Transition in Incompressible Flow
No full textThe fluid dynamics process leading to laminar-turbulent transition behind an isolated roughness element is investigated in the incompressible regime using particle image velocimetry. The study covers the effect of roughness size and geometry on the promotion of transition. The measurement domain covers a large streamwise range from the near wake to the onset of the turbulent regime. Planar PIV measurements reveal the basic flow pattern and the turbulent structure of the flow characterizing by the velocity fluctuation statistics (RMS of the streamwise and wall-normal velocity component and Reynolds shear stress). The high Reynolds shear stress level reaching the region near the wall in the downstream area indicates the onset of turbulent boundary layer
The L-p-to-L-q boundedness of commutators with applications to the Jacobian operator
No full textSupplying the missing necessary conditions, we complete the characterisation of the L-p -> L-q boundedness of commutators [b, T] of pointwise multiplication and Calderon-Zygmund operators, for arbitrary pairs of 1 q, our results are new even for special classical operators with smooth kernels. As an application, we show that every f is an element of L-p(R-d) can be represented as a convergent series of normalised Jacobians J(u) = det del uof u is an element of (over dot(W))(1,dp)(R-d)(d). This extends, from p = 1 to p > 1, a result of Coifman, Lions, Meyer and Semmes about J:. (over dot(W))(1,d)(R-d)(d) -> H-1(R-d), and supports a conjecture of Iwaniec about the solvability of the equation Ju = f is an element of L-p(R-d). (C) 2021 The Author(s). Published by Elsevier Masson SAS.Peer reviewe
Modification of Loop 1 Affects the Nucleotide Binding Properties of Myo1c, the Adaptation Motor in the Inner Ear
No full textMyo1c is one of eight members of the mammalian myosin I family of actin-associated molecular motors. In stereocilia of the hair cells in the inner ear, Myo1c presumably serves as the adaptation motor, which regulates the opening and closing of transduction channels. Although there is conservation of sequence and structure among all myosins in the N-terminal motor domain, which contains the nucleotide- and actin-binding sites, some differences include the length and composition of surface loops, including loop 1, which lies near the nucleotide-binding domain. To investigate the role of loop 1, we expressed in insect cells mutants of a truncated form of Myo1c, Myo1c1IQ, as well as chimeras of Myo1c1IQ with the analogous loop from other myosins. We found that replacement of the charged residues in loop 1 with alanines or the whole loop with a series of alanines did not alter the ATPase activity, transient kinetics properties, or Ca2+ sensitivity of Myo1c1IQ. Substitution of loop 1 with that of the corresponding region from tonic smooth muscle myosin II (Myo1c1IQ-tonic) or replacement with a single glycine (Myo1c1IQ-G) accelerated the release of ADP from A.M 2?3-fold in Ca2+, whereas substitution with loop 1 from phasic muscle myosin II (Myo1c1IQ-phasic) accelerated the release of ADP 35-fold. Motility assays with chimeras containing a single ?-helix, or SAH, domain showed that Myo1cSAH-tonic translocated actin in vitro twice as fast as Myo1cSAH-WT and 3-fold faster than Myo1cSAH-G. The studies show that changes induced in Myo1c via modification of loop 1 showed no resemblance to the behavior of the loop donor myosins or to the changes previously observed with similar Myo1b chimeras
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